The skipper is one of the key men missing, along with another injury victim, James Forrest and the suspended Efe Ambrose.
The talisman in Europe for the past two seasons, Georgios Samaras, is also now no longer there to come up with crucial goals.
But Brown has urged his team-mates to keep believing they have enough quality and experience of pressure-pot situations to get the club into Friday's Group Stage Play-off draw.
The man whose hamstring rupture will keep him out for a further two months said: "The players we do have are mostly the ones who were there last season when we got through some tough ties in the qualification for the Champions League.
"We are a good enough team, and a good enough squad to do it again. We have got to believe we can turn this round.
"If you don't believe, there is no point going out onto the park. Every team suffers disappointing results. That's when strong characters and good players come through."
Brown knows from experience that coming back from a first-leg result like the one suffered in Warsaw last week can galvanise a squad.
That was the case 12 months ago when they overcame a 2-0 play off defeat in Kazakhstan against Shakhter Karagandy to win through 3-0 on a dramatic night at Celtic Park.
After helping gee up his team-mates in the Murrayfield dressing room before the game, Brown will sit among the fans in the main stand and said: "Turning around a tie like this can definitely help bring a team even closer together.
"Last season, everyone wrote us off when we lost to Karagandy. But the fans turned out in their thousands and helped us achieve the result we needed."
There is no doubt that Brown's absence on the pitch in Poland was sorely missed as Legia defeated the Hoops' 10 men 4-1.
It left the Celtic players battered and their pride bruised. But the captain, who resumed light jogging yesterday, is confident they are not broken.
He said: "The spirit is always there. We don't like losing any game. When they do, they want to get back out there and make amends."
Brown's only note of caution is that if, as he expects, Celtic do drag themselves right back into the tie, they continue focusing and controlling the match to the final whistle.
The two goals shipped in the closing minutes in Warsaw have made a difficult task much tougher.
And the captain said: "No matter what happens this time, we have to stay organised for 90 minutes, play as well as we can but, above all, believe in ourselves because we can do this."